Question

5. Suppose the coffee industry claimed that the average adult drinks 1.7 cups of coffee per day. | |||||||||

To test this claim, a random sample of 10 Coffee drinkers were selected | |||||||||

and their average coffee consumption was found to be 2.0 cups per day. | |||||||||

Assume the standard deviation of daily coffee consumption per day is 0.5 cups. | |||||||||

Using α = 0.20 test the Hypothesis Is the Coffee consumption differs from the average coffee consumption? | |||||||||

a. State the Null Hypothesis and alternate Hypothesis. | |||||||||

b. use the Z statistical model test the Hypothesis at 0.10 significance level and the p value. | |||||||||

c. Is the coffee industry's claim supported by this sample? |

Answer #1

Population mean = U

Sample mean = x = 2 cups per day

Standard Deviation = s = 0.5 cups per day

Sample size = n = 10

Standard error of mean = se = s/n^{0.5} =
0.5/10^{0.5} = 0.16 cups per day

a) Hypotheses,

H0 : U = 1.7, against

H1 : U not = 1.7 (Two tailed test)

b) Zscore = (x - U)/se = (2 - 1.7)/0.16 = 1.875

p-value = 0.0304

As it is a two tailed test, so, comparing p-value with level of significance(a)/2 we get,

0.0304< 0.05

Thus, we reject the null hypothesis.

c) Hence, coffee industry’s claim that an adult consumes 1.7 cups of coffee per day on average is not supported by this sample.

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